Filter that minimizes in-band noise and maximizes detection sensitivity of exponentially-modulated signals

Abstract

Frequency domain (FDTF) and time domain (TDTF) trans-filters compress in-band AWGN, demodulate input signals and have no threshold due to applied noise. Two parallel frequency selective networks with opposite amplitude vs frequency slopes are designed to remain 180 degrees out of phase over the signal band in the FDTF whereas two parallel delay networks are used in the TDTF. Output amplitudes are equal at band center and are summed producing a monotonic amplitude vs frequency characteristic going thru zero at center frequency with abrupt phase reversal. This produces the parabolic output noise density and differentiates applied signals. Absence of nonlinear circuit components and product devices prevents generation of noise×noise products, avoiding the threshold phenomenon. Exponentially modulated digital signals produce output impulses due to the slope and abrupt phase reversal. The impulses have strong fundamental frequency components and may be recovered at baseband without frequency conversion. Cascading trans-filters increases noise reduction and impulse amplitude. The trans-filter algorithm may be used separately or in conjunction with one or more hardware trans-filters.

What is claimed is: 
     
       1. A filter that demodulates an exponentially-modulated signal, having noise in its signal band, and compresses the noise in its signal band, said filter comprising:
 a pair of parallel paths having a common input into which is fed the exponentially modulated signal and wherein at least one of said parallel paths comprises a time delay for delaying the exponentially-modulated signal passing therethrough, each of said parallel paths comprising a respective output signal and wherein said respective output signals are delayed in time from each other by a predetermined parameter, said parallel paths and said time delay comprising only linear components, said linear components minimizing a threshold that is normally present in exponentially-modulated signal demodulators that use non-linear components; 
 a summing network for receiving said respective output signals and summing said respective output signals to generate an output that is a function of a rate change of a carrier frequency of the exponentially-modulated signal, said output comprising impulses for abrupt changes in the carrier frequency corresponding to data transitions that form a baseband of said exponentially-modulated signal; and 
 wherein said filter is operative on any modulation format of said exponentially modulated signal and generates said impulses while compressing noise in the signal band. 
 
     
     
       2. The filter of  claim 1  wherein said filter comprises a center frequency and wherein said predetermined parameter comprises a reciprocal of twice the center frequency of said filter. 
     
     
       3. The filter of  claim 1  wherein each one of said parallel paths comprises a respective time delay, D 1  and D 2 , and wherein said predetermined parameter comprises a difference between D 1  and D 2  being equal to a reciprocal of twice the center frequency of said filter. 
     
     
       4. The filter of  claim 1  wherein said filter comprises a center frequency and wherein said respective output signals are 180° out of phase only at the center frequency of said filter. 
     
     
       5. The filter of  claim 1  wherein said output of said summing network comprises a comb band reject filter characteristic comprising a plurality of teeth that extracts a frequency derivative of the exponentially-modulated signal while reducing in-band noise at each tooth in the comb band reject filter characteristic. 
     
     
       6. The filter of  claim 5  wherein said comb band reject filter characteristic occurs whenever a difference in time delay between said respective output signals corresponds to an odd multiple of half periods of an input frequency of the exponentially-modulated signal. 
     
     
       7. The filter of  claim 6  wherein frequency spacing, F X , between said teeth in said comb band reject filter characteristic comprises a reciprocal of said difference in time delay between said respective output signals. 
     
     
       8. The filter of  claim 7  wherein a frequency of any tooth, F N , in said comb band reject filter characteristic is given by:
     F   N =(2 N− 1)( F   X /2), wherein  N  is any positive integer. 
 
     
     
       9. The filter of  claim 1  wherein the exponentially-modulated signal is a digitally modulated signal and wherein said filter asynchronously generates polarized impulses at data transitions of the digitally modulated signal. 
     
     
       10. A method for demodulating an exponentially-modulated signal, having noise in its signal band, and compressing the noise in its signal band, said method comprising:
 feeding the exponentially-modulated signal into a filter comprising a pair of parallel paths having a common input and wherein at least one of said parallel paths comprises a time delay for delaying the exponentially-modulated signal passing therethrough, each of said parallel paths comprising a respective output signal and wherein said respective output signals are delayed in time from each other by a predetermined parameter, said parallel paths and said time delay comprising only linear components, said linear components minimizing a threshold that is normally present in exponentially-modulated signal demodulators that use non-linear components; 
 summing said respective output signals to generate an output that is a function of a rate change of a carrier frequency of the exponentially-modulated signal, said output comprising impulses for abrupt changes in the carrier frequency corresponding to data transitions that form a baseband of said exponentially-modulated signal, said generation of impulses being independent of a modulation format used in said exponentially-modulated format; and 
 compressing noise in said signal band. 
 
     
     
       11. The method of  claim 10  wherein said filter comprises a center frequency and wherein said predetermined parameter comprises a reciprocal of twice the center frequency of said filter. 
     
     
       12. The method of  claim 10  wherein each one of said parallel paths comprises a respective time delay, D 1  and D 2 , and wherein said predetermined parameter comprises a difference between D 1  and D 2  being equal to a reciprocal of twice the center frequency of said filter. 
     
     
       13. The method of  claim 10  wherein said filter comprises a center frequency and wherein said respective output signals are 180° out of phase only at the center frequency of said filter. 
     
     
       14. The method of  claim 10  wherein said step of summing said respective output signals forms a comb band reject filter characteristic comprising a plurality of teeth that extracts a frequency derivative of the exponentially-modulated signal while reducing in-band noise at each tooth in the comb band reject filter characteristic whenever a difference in time delay between said respective output signals corresponds to an odd multiple of half periods of an input frequency of the exponentially-modulated signal. 
     
     
       15. The method of  claim 14  wherein frequency spacing, F X , between said teeth in said comb band reject filter characteristic comprises a reciprocal of said difference in time delay between said respective output signals. 
     
     
       16. The method of  claim 15  wherein a frequency of any tooth, F N , in said comb band reject filter characteristic is given by:
     F   N =(2 N− 1)( F   X /2), wherein  N  is any positive integer. 
 
     
     
       17. The method of  claim 14  wherein said step of forming a comb band reject filter characteristic allows for a rapid determination of the input frequency of the exponentially-modulated signal. 
     
     
       18. The method of  claim 17  wherein said step of forming a comb band reject filter characteristic allows for rapid threat location. 
     
     
       19. The method of  claim 10  further comprising the steps of:
 feeding said impulses into a second filter comprising a second pair of parallel paths having a common input and wherein at least one of said second parallel paths comprises a second time delay for delaying the impulses passing therethrough, each of said second parallel paths comprising a respective output signal and wherein said respective output signals of said second parallel paths are delayed in time from each other by said predetermined parameter, said second parallel paths and said second time delay comprising only linear components, said linear components minimizing said threshold that is normally present in exponentially-modulated signal demodulators that use non-linear components; and 
 summing said respective output signals of said second parallel paths to generate further impulses while compressing noise in the signal band and further increasing amplitudes of said impulses. 
 
     
     
       20. The method of  claim 19  wherein said predetermined parameter comprises a reciprocal of twice the center frequency of said first filter. 
     
     
       21. The method of  claim 19  wherein each one of said second parallel paths comprises a respective time delay, D 1  and D 2 , and wherein said predetermined parameter comprises a difference between D 1  and D 2  being equal to a reciprocal of twice said center frequency of said first filter. 
     
     
       22. The method of  claim 19  wherein said respective output signals of said second parallel signals are 180° out of phase only at the center frequency of said first filter. 
     
     
       23. A system, formed of at least two filters, that demodulates an exponentially-modulated signal, having noise in its signal band, and compresses the noise in its signal band, said system comprising:
 a first filter comprising:
 a first pair of parallel paths having a common input into which is fed the exponentially modulated signal and wherein at least one of said first parallel paths comprises a time delay for delaying the exponentially-modulated signal passing therethrough, each of said first parallel paths comprising a respective output signal and wherein said respective output signals are delayed in time from each other by a predetermined parameter, said parallel paths and said time delay comprising only linear components, said linear components minimizing a threshold that is normally present in exponentially-modulated signal demodulators that use non-linear components; 
 a first summing network for receiving said respective output signals from said first pair of parallel paths and summing said respective output signals to generate an output that is a function of a rate change of a carrier frequency of said exponentially-modulated signal, said output comprising impulses for abrupt changes in the carrier frequency corresponding to data transitions that form a baseband of said exponentially-modulated signal; and 
 wherein said first filter is operative on any modulation format of said exponentially modulated signal and generates said impulses while compressing noise in the signal band; and 
 
 
       a second filter comprising:
 a second pair of parallel paths having a common input into which said impulses are fed and wherein at least one of said second parallel paths comprises a time delay for delaying the impulses passing therethrough, each of said second parallel paths comprising a respective output signal and wherein said respective output signals of said second pair of parallel paths are delayed in time from each other by said predetermined parameter, said second pair of parallel paths and said time delay comprising only linear components, said linear components minimizing the threshold that is normally present in exponentially-modulated signal demodulators that use non-linear components; and 
 a second summing network for receiving said respective output signals from said second pair of parallel paths and summing said respective output signals to further increase amplitudes of said impulses for abrupt changes in the carrier frequency corresponding to data transitions that form the baseband of said exponentially-modulated signal while further compressing noise in the signal band. 
 
     
     
       24. The system of  claim 23  wherein said filter comprises a center frequency and wherein said predetermined parameter comprises a reciprocal of twice the center frequency of said first filter. 
     
     
       25. The system of  claim 23  wherein each one of said first and second parallel paths comprises a respective time delay, D 1  and D 2 , and wherein said predetermined parameter comprises a difference between D 1  and D 2  being equal to a reciprocal of twice the center frequency of said first filter. 
     
     
       26. The system of  claim 23  wherein said filter comprises a center frequency and wherein said respective output signals of said first parallel paths and said second parallel paths are 180° out of phase only at the center frequency of said first filter.